The temperature phase transition in the N-component scalar field theory with
spontaneous symmetry breaking is investigated in the perturbative approach. The
second Legendre transform is used together with the consideration of the gap
equations in the extrema of the free energy. Resummations are performed on the
super daisy level and beyond. The phase transition turns out to be weakly of
first order. The diagrams beyond the super daisy ones which are calculated
correspond to next-to-next-to-leading order in 1/N. It is shown that these
diagrams do not alter the phase transition qualitatively. In the limit N goes
to infinity the phase transition becomes second order. A comparison with other
approaches is done.Comment: 28 pages, 5 figures, corrected for some misprints, unnecessary
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